Finite Group Databasebeta

← #11860439

Subgroups — #11860439

Order 1152.

1022 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Dic3×#239C211yesmaximal, characteristic
2C2×#63943C211yesmaximal, characteristic
3D3×#887C211yesmaximal, characteristic, complemented
4#10592488C211yesmaximal, characteristic, complemented
5C3×#4803C211yesmaximal, characteristic
6C3×#4790C211yesmaximal, characteristic, complemented
7#10591582C211yesmaximal, characteristic, complemented
8#10591537C211yesmaximal, characteristic, complemented
9#10590948C211yesmaximal, characteristic, complemented
10#10590744C211yesmaximal, characteristic, complemented
11#10590743C211yesmaximal, characteristic, complemented
12Dic3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
13#10590580C211yesmaximal, characteristic, complemented
14#10590461C211yesmaximal, characteristic, complemented
15#10590453C211yesmaximal, characteristic, complemented
16C4×#918—31nomaximal
17#78867—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22#64096C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×#887C2211yescharacteristic
28#63943C418yescomplemented
29#63898—21no—
30#63898C2211yescharacteristic
31Dic3×D12—21no—
32Dic3×D12C2211yescharacteristic
33D3×Dic3⋊C4—21no—
34C4×D3×Dic3—21no—
35C4×D3×Dic3—21no—
36C4×D3×Dic3C2211yescharacteristic
37#63844C2211yescharacteristic
38#63843C2211yescharacteristic
39#63841—21no—
40#63841C2211yescharacteristic
41#63838—21no—
42#63837—21no—
43C2×#3716C2211yescharacteristic
44C2×#3715C2211yescharacteristic
45C2×#3711C2211yescharacteristic
46C32×#103C2211yescharacteristic
47#63643C2211yescharacteristic
48#63642C2211yescharacteristic
49#63635C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54C3×#809C2211yescharacteristic
55C3×#807C2211yescharacteristic
56#63576C2211yescharacteristic
57#63573C2211yescharacteristic
58#63567C2211yescharacteristic
59#63566C2211yescharacteristic
60#63555C2211yescharacteristic
61Dic3×C3⋊C8C2211yescharacteristic
62Dic3×#41—31no—
63C2×#951—31no—
64C2×#918—31no—
65C4×#239—31no—
66C4×D3×Q8—31no—
67C2×#887—31no—
68C3×C4×Q16—31no—
69C3×#417—31no—
70#5184—31no—
71#5120—31no—
72Dic3×M16—31no—
73C4×#216—31no—
74C4×#215—31no—
75#4964—31no—
76#4889—31no—
77#4881—31no—
78#4817—31no—
79#4803D311yescharacteristic
80#4802—31no—
81#4790—31no—
82#4790D311yescharacteristic, complemented
83#4789—31no—
84#4789—31no—
85#4789—31no—
86#4789—61no—
87#4758—31no—
88#4758—31no—
89#4757—31no—
90#4757—31no—
91C4×#204—31no—
92C4×ΓL(1,𝔽25)—31no—
93C2×C32×Q8C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C3×#239—22no—
96C3×#239C2×C414yes—
97C2×C3×D12—21no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×#627—21no—
104C2×D3×Dic3—21no—
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3D411yescharacteristic
108C2×D3×Dic3D411yescharacteristic
109D3×Dic6—22no—
110D3×Dic6C2×C414yescomplemented
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113#3756C2×C414yescomplemented
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117C4×C3⋊Dic3—21no—
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#216C2×C414yescomplemented
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×C4×Dic3—21no—
128C3×C4×Dic3—21no—
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×ΓL(1,𝔽25)—22no—
133#3724—21no—
134Dic3⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139Dic32—21no—
140Dic32—21no—
141Dic32D411yescharacteristic
142Dic32D411yescharacteristic
143#3716C2×C414yescomplemented
144#3715C2×C414yescomplemented
145#3711C2×C414yescomplemented
146C4×#137—91noSylow
147C2×C3×#41—31no—
148C2×#239C2×D311yescharacteristic
149C2×D3×Q8—31no—
150C22×Dic6—31no—
151C2×C3×Q16—31no—
152C2×C3×M16—31no—
153C3×C4×Q8—31no—
154C3×C4×Q8—31no—
155C2×C3×C4⋊C4—31no—
156#951—38no—
157Q8×Dic3—31no—
158Q8×Dic3—31no—
159Q8×Dic3—31no—
160Q8×Dic3—61no—
161Q8×Dic3C2×D311yescharacteristic
162C2×#216—31no—
163C2×#216—31no—
164C2×#216—61no—
165C2×#216C2×D311yescharacteristic
166C2×#215—31no—
167D4×Dic3—31no—
168D4×Dic3—31no—
169D4×Dic3—61no—
170D4×Dic3—61no—
171C2×#214—31no—
172C2×#214—31no—
173#926—31no—
174#926—61no—
175C2×Dic3⋊C4—61no—
176C2×C4×Dic3—31no—
177C2×C4×Dic3—61no—
178C2×C4×Dic3—61no—
179C2×#208—31no—
180#918—38no—
181C2×#204—31no—
182C2×ΓL(1,𝔽25)—31no—
183C2×ΓL(1,𝔽25)C2×D311yescharacteristic
184#893—31no—
185#893—61no—
186#892—31no—
187#892—61no—
188D3×C4⋊C4—61no—
189D3×C4⋊C4C2×D311yescharacteristic
190#887—31no—
191#887—31no—
192#887—31no—
193#887—31no—
194#887—61no—
195#887—61no—
196#887—61no—
197#887—61no—
198#887C2×D311yescharacteristic
199C4×D12—31no—
200C4×D12—61no—
201C42×D3—31no—
202C42×D3—61no—
203C42×D3—61no—
204C4×Dic6—31no—
205C4×Dic6—61no—
206C3×#107—31no—
207C3×#103—21no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103C2×D311yescharacteristic
211C3×#103C2×D311yescharacteristic
212C3×#102—31no—
213C3×#102—31no—
214C3×C4×C8—31no—
215#835—31no—
216#835C2×D311yescharacteristic
217#821C2×D311yescharacteristic
218#817—31no—
219#816—31no—
220#816—31no—
221#816—31no—
222#816—31no—
223#816—61no—
224#816C2×D311yescharacteristic
225#815—31no—
226#815—31no—
227#815—31no—
228#815—31no—
229#815—61no—
230C8×Dic3—31no—
231C8×Dic3C2×D311yescharacteristic
232#810—31no—
233#809C2×D311yescharacteristic
234#808—31no—
235#808—31no—
236#808—31no—
237#808—61no—
238#807—31no—
239#807—31no—
240#807C2×D311yescharacteristic
241C4×C3⋊C8—31no—
242C22×C3×D3—21no—
243C22×C3×D3C2×D411yescharacteristic
244C32×Q8—21no—
245C32×Q8C22×C412yes—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253#634—21no—
254#634C22×C412yes—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—24no—
262C3×D12—21no—
263C3×D12C22×C412yes—
264C3×C4×D3—24no—
265C3×C4×D3—42no—
266C3×C4×D3C22×C412yes—
267C3×C4×D3#4112yes—
268C3×Dic6—21no—
269C3×Dic6C22×C412yes—
270#627—24no—
271D3×Dic3—24no—
272D3×Dic3—22no—
273D3×Dic3—41no—
274D3×Dic3—42no—
275D3×Dic3—42no—
276C32×C8—21no—
277C3⋊(C3⋊C8)C22×C412yes—
278C3×C3⋊C8—21no—
279C3×C3⋊C8C22×C412yes—
280C2×#137—91no—
281C4×#41—91no—
282C2×C4×Q8—91no—
283#441—91no—
284#441—91no—
285#440—91no—
286#440—91no—
287C4×Q16—31no—
288C4×Q16—91no—
289C4×SD16—91no—
290C4×SD16—91no—
291#428—91no—
292#419—91no—
293#417—31no—
294C4×M16—91no—
295C3×#41—34no—
296C3×#41—62no—
297C2×C3×Q8—21no—
298C2×C3×Q8—31no—
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×D4—31no—
302C2×C3×D4—61no—
303C22×C3×C4—31no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C22×Dic3—31no—
307C22×Dic3—31no—
308C22×Dic3—61no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311#239—22no—
312#239C4×D314yes—
313D3×Q8—34no—
314D3×Q8—62no—
315C2×D12—21no—
316C2×D12C22×D311yescharacteristic
317C2×C4×D3—21no—
318C2×C4×D3—21no—
319C2×C4×D3—31no—
320C2×C4×D3—31no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3C22×D311yescharacteristic
325C2×Dic6—31no—
326C2×Dic6—31no—
327C2×Dic6—34no—
328C2×Dic6—61no—
329C2×Dic6—62no—
330C2×Dic6—61no—
331C2×Dic6—61no—
332C2×Dic6C22×D311yescharacteristic
333C3×Q16—34no—
334C3×M16—62no—
335C2×C3×C8—21no—
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C3×C4⋊C4—21no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C42—31no—
349C3×C42—61no—
350C3×C42—61no—
351#217—61no—
352#217—61no—
353#217—61no—
354#216—34no—
355#216—34no—
356#216—64no—
357#216C4×D314yescomplemented
358#215—34no—
359#214—34no—
360#214—34no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364C4⋊Dic3—21no—
365C4⋊Dic3—31no—
366C4⋊Dic3—31no—
367C4⋊Dic3—61no—
368C4⋊Dic3—61no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—121no—
372C4⋊Dic3C22×D311yescharacteristic
373C4⋊Dic3C22×D311yescharacteristic
374Dic3⋊C4—21no—
375Dic3⋊C4—21no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—121no—
382C4×Dic3—21no—
383C4×Dic3—21no—
384C4×Dic3—31no—
385C4×Dic3—31no—
386C4×Dic3—31no—
387C4×Dic3—31no—
388C4×Dic3—31no—
389C4×Dic3—31no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—121no—
402C4×Dic3—121no—
403C4×Dic3C22×D311yescharacteristic
404#208—34no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410#204—34no—
411ΓL(1,𝔽25)—22no—
412ΓL(1,𝔽25)—34no—
413C22×C32C22×D411yescharacteristic
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—22no—
417C2×C3×D3—41no—
418C2×C3×D3—41no—
419C2×C3×D3C4×D412yes—
420C32×C4—22no—
421C32×C4—41no—
422C32×C4C23×C411yescharacteristic
423C32×C4C2×#4111yescharacteristic
424C3⋊Dic3—22no—
425C3⋊Dic3—21no—
426C3⋊Dic3—21no—
427C3⋊Dic3—41no—
428C3×Dic3—22no—
429C3×Dic3—21no—
430C3×Dic3—41no—
431C3×Dic3—41no—
432C3×Dic3C4×D412yes—
433C3×Dic3#13712yescomplemented
434C2×#41—31no—
435C22×Q8—91no—
436#137—98no—
437C2×Q16—31no—
438C2×Q16—91no—
439C2×SD16—91no—
440C2×SD16—91no—
441C2×M16—31no—
442C2×M16—91no—
443C4×Q8—31no—
444C4×Q8—31no—
445C4×Q8—91no—
446C4×Q8—91no—
447C4×Q8—91no—
448C4×Q8—91no—
449C4×Q8—181no—
450C4×Q8—181no—
451C4×D4—91no—
452C4×D4—91no—
453C4×D4—181no—
454C4×D4—181no—
455#117—91no—
456#117—181no—
457C2×C4⋊C4—31no—
458C2×C4⋊C4—181no—
459C2×C42—91no—
460C2×C42—181no—
461C2×C42—181no—
462#107—31no—
463#107—91no—
464#106—91no—
465#106—91no—
466#103—31no—
467#103—31no—
468#103—91no—
469#103—91no—
470#103—91no—
471#103D3211yescharacteristic
472#102—31no—
473#102—31no—
474#97—91no—
475#97—91no—
476C4×C8—31no—
477C4×C8—91no—
478C23×C3—31no—
479C23×C3—61no—
480C22×D3—21no—
481C22×D3D3×D411yescharacteristic
482C3×Q8—21no—
483C3×Q8—21no—
484C3×Q8—22no—
485C3×Q8—32no—
486C3×Q8—41no—
487C3×Q8—61no—
488C3×Q8C2×C4×D312yes—
489C3×Q8C2×C4×D312yes—
490C3×D4—32no—
491C3×D4—64no—
492C3×D4—61no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—32no—
501C2×C3×C4—32no—
502C2×C3×C4—31no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—64no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—122no—
510C2×C3×C4C23×D311yescharacteristic
511C2×C3×C4C23×D311yescharacteristic
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—31no—
516C2×Dic3—31no—
517C2×Dic3—31no—
518C2×Dic3—31no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—64no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—62no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—121no—
528C2×Dic3—121no—
529C2×Dic3—121no—
530C2×Dic3—122no—
531C2×Dic3—122no—
532C2×Dic3D3×D411yescharacteristic
533C2×Dic3D3×D411yescharacteristic
534C2×Dic3D3×D411yescharacteristic
535D12—24no—
536D12—21no—
537D12C2×C4×D312yes—
538C4×D3—24no—
539C4×D3—42no—
540C4×D3—62no—
541C4×D3—64no—
542C4×D3—121no—
543C4×D3—122no—
544C4×D3—122no—
545C4×D3C2×C4×D312yes—
546C4×D3#23712yes—
547Dic6—21no—
548Dic6—32no—
549Dic6—32no—
550Dic6—62no—
551Dic6—64no—
552Dic6—61no—
553Dic6—61no—
554Dic6—64no—
555Dic6—121no—
556Dic6C2×C4×D312yes—
557C3×C8—21no—
558C3×C8—21no—
559C3×C8—32no—
560C3×C8—41no—
561C3×C8—61no—
562C3⋊C8—21no—
563C3⋊C8—32no—
564C3⋊C8—32no—
565C3⋊C8—62no—
566C3⋊C8C2×C4×D312yes—
567C2×C32C2×C4×D411yescharacteristic
568C2×C32C2×#13711yescharacteristic
569C2×C32#57511yescharacteristic
570C3×D3—22no—
571C3×D3—42no—
572#41—34no—
573#41—62no—
574C2×Q8—31no—
575C2×Q8—94no—
576C2×Q8—91no—
577C2×Q8—181no—
578C2×Q8—182no—
579C2×Q8C2×D3211yescharacteristic
580C2×D4—31no—
581C2×D4—61no—
582C22×C4—31no—
583C22×C4—61no—
584C22×C4—61no—
585C22×C4—91no—
586C22×C4—91no—
587C22×C4—181no—
588C22×C4—181no—
589C22×C4—181no—
590Q16—34no—
591Q16—94no—
592SD16—94no—
593SD16—94no—
594M16—62no—
595M16—94no—
596C2×C8—31no—
597C2×C8—31no—
598C2×C8—91no—
599C2×C8C2×D3211yescharacteristic
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—91no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4C2×D3211yescharacteristic
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C42—31no—
615C42—61no—
616C42—61no—
617C42—91no—
618C42—91no—
619C42—91no—
620C42—181no—
621C42—181no—
622C42—181no—
623C42—181no—
624C42—181no—
625C22×C3—21no—
626C22×C3—32no—
627C22×C3—61no—
628C22×C3—61no—
629C22×C3—62no—
630C22×C3—121no—
631C22×C3—121no—
632C22×C3C2×D3×D411yescharacteristic
633C22×C3C2×D3×D411yescharacteristic
634C2×D3—21no—
635C2×D3—21no—
636C2×D3—22no—
637C2×D3—41no—
638C2×D3—41no—
639C2×D3#67⋊C412yes—
640C3×C4—22no—
641C3×C4—22no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—32no—
645C3×C4—32no—
646C3×C4—42no—
647C3×C4—41no—
648C3×C4—41no—
649C3×C4—62no—
650C3×C4—61no—
651C3×C4—81no—
652C3×C4—121no—
653C3×C4—121no—
654C3×C4C22×C4×D311yescharacteristic
655C3×C4C22×C4×D311yescharacteristic
656C3×C4C2×#23711yescharacteristic
657C3×C4D3×#4111yescharacteristic
658Dic3—21no—
659Dic3—22no—
660Dic3—41no—
661Dic3—41no—
662Dic3—62no—
663Dic3—61no—
664Dic3—61no—
665Dic3—61no—
666Dic3—61no—
667Dic3—62no—
668Dic3—122no—
669Dic3—121no—
670Dic3—121no—
671Dic3—121no—
672Dic3—121no—
673Dic3—241no—
674Dic3#67⋊C412yes—
675Dic3#91812yescomplemented
676C32C4×#13711yescharacteristic, complemented, Sylow
677C23—31no—
678C23—61no—
679Q8—21no—
680Q8—32no—
681Q8—61no—
682Q8—92no—
683Q8—184no—
684Q8—181no—
685Q8C4×D3212yes—
686D4—32no—
687D4—64no—
688D4—61no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—31no—
692C2×C4—31no—
693C2×C4—32no—
694C2×C4—32no—
695C2×C4—31no—
696C2×C4—64no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—91no—
701C2×C4—91no—
702C2×C4—122no—
703C2×C4—182no—
704C2×C4—184no—
705C2×C4—181no—
706C2×C4—181no—
707C2×C4—362no—
708C2×C4—361no—
709C2×C4—362no—
710C2×C4C22×D3211yescharacteristic
711C8—21no—
712C8—32no—
713C8—61no—
714C8—92no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—62no—
719C2×C3—122no—
720C2×C3C2×#67⋊C411yescharacteristic
721C2×C3C4×D3×D411yescharacteristic
722C2×C3C2×#91811yescharacteristic
723C2×C3#576811yescharacteristic
724C2×C3#577311yescharacteristic
725C2×C3D3×#13711yescharacteristic
726D3—22no—
727D3—42no—
728C22—32no—
729C22—61no—
730C22—61no—
731C22—62no—
732C22—121no—
733C22—121no—
734C22D32×D411yescharacteristic
735C4—22no—
736C4—32no—
737C4—32no—
738C4—41no—
739C4—61no—
740C4—62no—
741C4—121no—
742C4—121no—
743C4—181no—
744C4—181no—
745C4—182no—
746C4—361no—
747C4C2×C4×D3211yescharacteristic
748C4D3×#23711yescharacteristic
749C3—21no—
750C3#7886711yescharacteristic, complemented
751C3C4×#91811yescharacteristic, complemented
752C2—62no—
753C2—122no—
754C2D3×#67⋊C411yescharacteristic
755C2#1059474511yescharacteristic
756C2D3×#91811yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×C3×#239C22
cosocleC2×C32×C4C24
hypercenter#103D32
hypocenterC32C4×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. D3×#887C2semidirect
4. #10592488C2semidirect
6. C3×#4790C2semidirect
7. #10591582C2semidirect
8. #10591537C2semidirect
9. #10590948C2semidirect
10. #10590744C2semidirect
11. #10590743C2semidirect
12. Dic3×ΓL(1,𝔽25)C2semidirect
13. #10590580C2semidirect
14. #10590461C2semidirect
15. #10590453C2semidirect
28. #63943C4semidirect
82. #4790D3semidirect
110. D3×Dic6C2×C4semidirect
113. #3756C2×C4semidirect
121. C3×#216C2×C4semidirect
143. #3716C2×C4semidirect
144. #3715C2×C4semidirect
145. #3711C2×C4semidirect
357. #216C4×D3semidirect
433. C3×Dic3#137semidirect
675. Dic3#918semidirect
676. C32C4×#137semidirect
750. C3#78867semidirect
751. C3C4×#918semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
Dic3×#2392
C2×#639432
D3×#8872
#105924882
C3×#48032
C3×#47902
#105915822
#105915372
#105909482
#105907442
#105907432
Dic3×ΓL(1,𝔽25)2
#105905802
#105904612
#105904532
C4×#9183
#788673